Q: A wind turbine with 45-m radius blades extracts 40% of the kinetic energy from 98,000 kg of air moving at 11 m/s every second. How much energy is extracted per second?

$$E = 0.4 \times \frac{1}{2} \times 98,000 \times (11)^2$ = 2.4 \times 10^6$\ \mathrm{J}$$

Q: Bethany, who weighs 560 N, lies in a hammock. The left rope makes a 45° angle with the ground, and the right rope makes a 30° angle. What is the tension in the left rope?

$$T_{\text{left}} = 500\ \mathrm{N}$$

Q: A 0.15 kg baseball is thrown at 35 m/s at a 30° angle. What is its kinetic energy at the start of its motion?

$$K_i = \frac{1}{2} \times 0.15 \times (35)^2$ = 92\ \mathrm{J}$$

Q: A 0.15 kg baseball is thrown at 35 m/s at a 30° angle. What is its kinetic energy at the highest point of its arc?

$$K_{\text{peak}} = \frac{1}{2} \times 0.15 \times (35 \cos 30^\$$circ)^2$$ = 69\ \mathrm{J}$$

Q: A muscle fiber 2.0 cm long and $$3.1 \times 10$$^{-9}$$\ \mathrm{m}^2 in $$cross-section pulls with a force of 1.2 mN and contracts to 1.6 cm. What is the work done by the muscle fiber?

$$W = F \Delta x = 1.2 \times 10$$^{-3}$$ \times (0.016 - 0.02) = 4.8 \times 10$$^{-6}$$\ \mathrm{J}$$

Q: A meteor of mass 2.5 g enters the atmosphere at 40 km/s. At what speed would a 900-kg car have the same kinetic energy?

$$v = \sqrt{\frac{1}{2} m_{\text{meteor}} v_{\text{meteor}}^2 / (\frac{1}{2} m_{\text{car}})} = 67\ \mathrm{m/s}$$

Q: A double-decker bus has a track width of 2.05 m and a center of gravity height of 1.45 m when empty. What is the critical angle for rollover?

$$\theta_c = \tan$$^{-1}$$\left(\frac{2.05}{2 \times 1.45}\right) = 35.3^\circ$$

Q: A crate slides 2.5 m down a ramp at 20° while Paige pushes back with a 76 N horizontal force. How much work does Paige do?

$$W = F d \cos \theta = -180\ \mathrm{J}$$

Q: A 255-kg piano is lowered 4 m by two ropes. How much work is done by gravity?

$$W = mgh = 255 \times 9.8 \times 4 = 1.0 \times 10^4$\ \mathrm{J}$$

Q: The spring in a retractable pen is 1.8 cm long with a 300 N/m spring constant. When compressed by 1.0 mm, you click to compress it by an additional 6.0 mm. How much energy is required to extend the pen?

$$U_s = \frac{1}{2} k (x_2$^2 - x_1$^2) = 7.20 \times 10$$^{-3}$$\ \mathrm{J}$$

Question 1

A wind turbine with 45-m radius blades extracts 40% of the kinetic energy from 98,000 kg of air moving at 11 m/s every second. How much energy is extracted per second?

Accepted Answer

$$E = 0.4 	imes \frac{1}{2} 	imes 98,000 	imes (11)^2$ = 2.4 	imes 10^6$\ \mathrm{J}$$

Question 2

Bethany, who weighs 560 N, lies in a hammock. The left rope makes a 45° angle with the ground, and the right rope makes a 30° angle. What is the tension in the left rope?

Accepted Answer

$$T_{	ext{left}} = 500\ \mathrm{N}$$

Question 3

A 0.15 kg baseball is thrown at 35 m/s at a 30° angle. What is its kinetic energy at the start of its motion?

Accepted Answer

$$K_i = \frac{1}{2} 	imes 0.15 	imes (35)^2$ = 92\ \mathrm{J}$$

Question 4

A 0.15 kg baseball is thrown at 35 m/s at a 30° angle. What is its kinetic energy at the highest point of its arc?

Accepted Answer

$$K_{	ext{peak}} = \frac{1}{2} 	imes 0.15 	imes (35 \cos 30^\$$circ)^2$$ = 69\ \mathrm{J}$$

Question 5

How close to the right edge of a 56-kg picnic table can an 85-kg man stand without tipping the table, if the table is 2.0 m long?

Accepted Answer

$$d = 0.22\ \mathrm{m}$$

Question 6

A muscle fiber 2.0 cm long and $$3.1 	imes 10$$^{-9}$$\ \mathrm{m}^2 in $$cross-section pulls with a force of 1.2 mN and contracts to 1.6 cm. What is the work done by the muscle fiber?

Accepted Answer

$$W = F \Delta x = 1.2 	imes 10$$^{-3}$$ 	imes (0.016 - 0.02) = 4.8 	imes 10$$^{-6}$$\ \mathrm{J}$$

Question 7

A meteor of mass 2.5 g enters the atmosphere at 40 km/s. At what speed would a 900-kg car have the same kinetic energy?

Accepted Answer

$$v = \sqrt{\frac{1}{2} m_{	ext{meteor}} v_{	ext{meteor}}^2 / (\frac{1}{2} m_{	ext{car}})} = 67\ \mathrm{m/s}$$

Question 8

A double-decker bus has a track width of 2.05 m and a center of gravity height of 1.45 m when empty. What is the critical angle for rollover?

Accepted Answer

$$	heta_c = 	an$$^{-1}$$\left(\frac{2.05}{2 	imes 1.45}ight) = 35.3^\circ$$

Question 9

A crate slides 2.5 m down a ramp at 20° while Paige pushes back with a 76 N horizontal force. How much work does Paige do?

Accepted Answer

$$W = F d \cos 	heta = -180\ \mathrm{J}$$

Question 10

A hockey puck compresses a spring by 1.0 cm when it hits at speed $$v. $$What will be the maximum compression if the puck hits at $$2v$$?

Accepted Answer

$$x = 3.6\ \mathrm{cm}$$

Question 11

A woman pushes a 110-kg wheelbarrow with its center of gravity 0.35 m behind the axle and supports it at handles 1.1 m behind the axle. What is the force required to support the wheelbarrow?

Accepted Answer

$$F = 340\ \mathrm{N}$$

Question 12

A sign of mass 8.4 kg hangs from a cable at 60° to the horizontal. What is the tension in the cable?

Accepted Answer

$$T = 165\ \mathrm{N}$$

Question 13

A 255-kg piano is lowered 4 m by two ropes. How much work is done by gravity?

Accepted Answer

$$W = mgh = 255 	imes 9.8 	imes 4 = 1.0 	imes 10^4$\ \mathrm{J}$$

Question 14

The spring in a retractable pen is 1.8 cm long with a 300 N/m spring constant. When compressed by 1.0 mm, you click to compress it by an additional 6.0 mm. How much energy is required to extend the pen?

Accepted Answer

$$U_s = \frac{1}{2} k (x_2$^2 - x_1$^2) = 7.20 	imes 10$$^{-3}$$\ \mathrm{J}$$

Question 15

The world's fastest humans can reach speeds of about 11 m/s. To increase gravitational potential energy by an amount equal to their kinetic energy at full speed, how high would they need to climb?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(11)^2$}{2 	imes 9.8} = 6.2\ \mathrm{m}$$

Question 16

A 1400-kg wrecking ball hangs from a 14-m cable and is pulled back until the cable makes a 22° angle with the vertical. By how much has the gravitational potential energy changed?

Accepted Answer

$$\Delta U = mgh = 1.4 	imes 10^4$\ \mathrm{J}$$

Question 17

A block slides down a smooth ramp from height $$h$$ and reaches speed $$v at $$the bottom. At what height is its speed equal to $$v/2 on a $$second ramp?

Accepted Answer

$$h/4$$

Question 18

A fan puts 1.8 W of kinetic energy into the air every second. If the fan speed is doubled and it moves twice as much air at twice the speed, how much kinetic energy goes into the air every second?

Accepted Answer

$$P = 1.8 	imes 8 = 14\ \mathrm{W}$$

Question 19

A flywheel stores a maximum of 4.9 MJ at 19,000 rpm. What is its moment of inertia?

Accepted Answer

$$I = 2.5\ \mathrm{kg \cdot m^2$}$$

Physics Homework 8: Step-by-Step Study Guidance

Study Guide - Practice Questions

Study Guide - Flashcards